Solve 25/3*(2/5-1)^2*(5/3-2)^2+(1/2-1)^2

$$\frac { 25 } { 3 } \cdot ( \frac { 2 } { 5 } - 1 ) ^ { 2 } \cdot ( \frac { 5 } { 3 } - 2 ) ^ { 2 } + ( \frac { 1 } { 2 } - 1 ) ^ { 2 }$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Subtract 1 from \frac{2}{5} to get -\frac{3}{5}.

$$\frac{25}{3}\left(-\frac{3}{5}\right)^{2}\left(\frac{5}{3}-2\right)^{2}+\left(\frac{1}{2}-1\right)^{2}$$

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{25}{3}\times \frac{9}{25}\left(\frac{5}{3}-2\right)^{2}+\left(\frac{1}{2}-1\right)^{2}$$

Multiply \frac{25}{3} and \frac{9}{25} to get 3.

$$3\left(\frac{5}{3}-2\right)^{2}+\left(\frac{1}{2}-1\right)^{2}$$

Subtract 2 from \frac{5}{3} to get -\frac{1}{3}.

$$3\left(-\frac{1}{3}\right)^{2}+\left(\frac{1}{2}-1\right)^{2}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$3\times \frac{1}{9}+\left(\frac{1}{2}-1\right)^{2}$$

Multiply 3 and \frac{1}{9} to get \frac{1}{3}.

$$\frac{1}{3}+\left(\frac{1}{2}-1\right)^{2}$$

Subtract 1 from \frac{1}{2} to get -\frac{1}{2}.

$$\frac{1}{3}+\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{3}+\frac{1}{4}$$

Add \frac{1}{3} and \frac{1}{4} to get \frac{7}{12}.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$